The 23-year-old shooting guard, whom the team drafted in the first-round in 2010, was a top target partly because the Celtics lacked the salary cap space to go after other big-name free agents.

But Celtics president of basketball operations Danny Ainge also considers Bradley — one of the NBA’s top perimeter defenders — to be a key part of the team’s future. Ainge had stated that again Monday, saying, “I think Avery can be a very key player in us winning the championship.”

Bradley also made it clear that same day that he wanted to stay in Boston, saying at a local basketball camp that “I want to be here. And I let [the Celtics] know that. When the time comes, we’ll just see what happens, and see if we come to an agreement.”

Before free agency opened, the Celtics had extended a $3.6 million qualifying offer to Bradley, making him a restricted free agent and allowing the Celtics to match any offer team’s offer.

“Avery’s glad to be back in Boston,” said Bradley’s agent, Mitchell Butler. “We’re very happy he remains a Celtic.”

Around the league, there was mixed reaction to Bradley’s signing, particularly because the price tag was considered by some to be too high.

“Way too high,” said one league source. “I was shocked by that one, especially with [first-round draft pick] Marcus Smart on board now.”

Said another league source, “Too high, but they could not afford to lose him.”

Bradley and his camp turned down a four-year, $26 million extension last year according to multiple reports – and it ultimately paid off for him, quite literally.

But a key factor, other league sources said, was Bradley’s market value. After former Lakers guard Jodie Meeks recently agreed to a three-year deal worth $19.5 million with the Pistons, it seemed likely that Bradley’s price tag might increase. And apparently, it did.

“It’s fair both ways — if Meeks can get $19 million, then [Bradley’s salary] is about right,” one source said.

Said another league source, “Hey, Jodie Meeks for $6.5 million per year is a joke and Bradley is a hell of a lot better than him.”

By offering Bradley a rather handsome sum early on in free agency, the Celtics ensured that they’d lock up their top target rather than waiting things out and letting other teams start a possible bidding war for a promising young guard the Celtics believe will only improve.

Last season, his fourth in the NBA, Bradley averaged a career-high 14.9 points along with 3.8 rebounds, 1.4 assists, and 1.1 steals over 30.9 minutes per game in 60 appearances. He also shot nearly 40 percent from 3-point range.

Most importantly, Bradley became much more of the offensive threat that the Celtics hoped for, averaging 15.6 points per game in December and then 16.3 in January.

But injuries crept in, as they often have throughout Bradley’s career. He missed 22 games this past season because of ankle issues. Bradley also missed 31 games the season before while recovering from dual shoulder surgeries.

Bradley, a former University of Texas standout, has not played more than 64 games in an 82-game regular-season schedule, which has earned him the label “injury-prone.”

Ainge said late last season that the biggest issue with Bradley is, of course, injuries.

“He plays hard and he’s had some injuries,” Ainge said, “but none of them are injuries that should prevent him from being a great player.”

Still, one league source said, “You just drafted Marcus Smart, so eventually [Bradley] is going to be your third guard. Eight million per year for a third guard is crazy.”

Ainge stressed last week when the team drafted Smart with the No. 6 overall pick out of Oklahoma State that he thinks the Celtics can have a three-guard rotation with Rajon Rondo, Bradley, and Smart splitting the bulk of the minutes.

Though Celtics forward Jared Sullinger couldn’t discuss Bradley’s new deal until it becomes official, Sullinger did talk about what impact Bradley has made on the team.

“He was a great defender,” Sullinger said after the Celtics’ summer league squad held a practice at the team’s facility in Waltham Wednesday. “He made a lot of things easy for us defensively. Guarding screens sometimes, you didn’t have to guard them because Avery would kind of push himself through the screen. He made life real easy for me.”

Smart also praised Bradley, a fellow defensive instigator.

“As a competitor, you want somebody who’s going to be out there and competing with you and have your back, not only on the offensive end, but on the defensive end,” Smart said. “Avery does that. He holds himself and everybody else accountable.”

Ultimately, signing Bradley was the surest move the Celtics could make at this point in the free agency period, allowing them to secure a key member of their backcourt.

But the NBA remains an uncertain landscape at the moment with LeBron James and Carmelo Anthony still considering their options, which puts several other teams in a holding pattern.

The Celtics still hope to add players via the trade route, their most likely avenue of adding proven talent considering their rather limited financial flexibility, which became even more limited after agreeing to terms with Bradley.

And ever looming is the possibility of a trade with the Minnesota Timberwolves for All-Star forward Kevin Love, though it’s unclear if the Timberwolves are truly ready to deal him — and just which team can offer the best deal.